Coventry have finally accepted a bid from the St Andrews club after rejecting four earlier offers for the 24-year-old.
McSheffrey passed a Blues medical on Tuesday and has signed a four-year deal with the option of a further two years.
McSheffrey has come through the ranks at Coventry and scored 17 goals for the Sky Blues last season.
Coventry managing director Paul Fletcher says the decision was made after consultations between the "board, manager and the player himself".
"It was never our intention to let Gary go but we have made a decision which we believe is in the best interests of the club," he told the club's website.
"Gary has been a tremendous servant to the club but there comes a time in everyone's career when they have the opportunity to move on.
"Although I understand that this decision will be unpopular with many of our supporters, I would urge all of our fans to look long-termn towards our goal of reaching the Premiership within the next three years.
"This money will help manager Micky Adams to strengthen the squad and create a better team to get us there."
WHat the hell this is insane